Hodgdon, which makes 777, does not list loads on its website for the Walker.
However, it lists a maximum of 35 grains for the Ruger Old Army. This is with a .457 ball and felt Wonder Wad between powder and ball.
Hodgdon notes:
Triple Seven is a high energy product designed to provide the muzzleloading hunter with higher velocities when used in the same VOLUME as blackpowder. To duplicate a blackpowder load velocity using Triple Seven, you must decrease the powder charge by 15%.
I would not exceed 35 grains in the Walker, regardless of what you are told by anyone other than Hodgdon.
After all, Hodgdon makes the stuff. It has the ballistics lab with sophisticated equipment to measure pressures. Hodgdon also has the trained people to interpret the data obtained from the tests.
Cap and ball revolvers lack a cartridge case (duh) to measure and obtain even the merest inkling of when you're generating dangerous pressure.
Typically, the best indicator is when the copper caps fragment into numerous pieces because of high pressure coming back through the nipple.
Increase the pressure and the hammer may be blown back to half cock. Increase it even more, and the nipple can strip its threads and fly back at your face.
These are all high-pressure instances.
Nipples with flame channels too large will also cause caps to fragment badly, but won't force the hammer back.
With the above in mind -- especially the lack of a cartridge case to measure after firing -- any estimation of pressure is pure guesswork.
Just because your revolver takes the load doesn't make it safe. It may take a dozen shots, or a hundred, but high-pressure loads can and eventually will damage or destroy your revolver.
The Walker was quickly replaced by the Dragoon because of its faults. It is hardly the epitome of cap and ball revolver design, but rather closer to a prototype from which much was learned.
The Dragoons that followed it had better catches for the rammer, and reduced capacity chambers. The metallurgy of then was inferior to today's, but even the best steel has pressure limits.
Stick to black powder if you must load the Walker's chambers with as much as they will hold. Hodgdon 777 is not designed for experimentation by shooters; it must be used as specified.
Those specifications are based on measured pressures, not guesswork.